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Assignment No.1 (Course STA 406)

Fall 2014 (Total Marks15)

The assignment is being uploaded to build up the concepts about the point estimation and confidence interval.

Question 1:(Marks: 2+5=7)

a. Let UandVare two unbiased estimators ofλand Variance (U) ≤ Variance (V), then which estimator is more efficient and why?

b. A mobile company XYZ wants to conduct a survey to find the proportion P of those customers that are happy with the purchase of their new mobile phone. The company took a random sample of 1000 customers who recently purchased the new mobile phone. They found that among those, 400 customers were happy with their purchase. Find the 95% Confidence Interval for P?

Question 2:

a. An independent random sample of 50 and 70 animals from two farms show the average animal weight to be 50 kg and 40 kg with standard deviation of 2.5 kg and 1.5 kg respectively. Assuming normality, construct a 95% confidence interval for the expected difference in the weights.

b. The standard deviation of the lifetime of certain TV picture tubes is estimated as 150 hours. How much large a sample must be taken in order to be 99% confident that the error in the estimated means lifetime will not exceed 25 hours.

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